Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Dr. Nathan Perlmutter
Stanford University

 
spricht am
 
Montag, 24. Juli 2017
 
um
 
16:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Parametrized Morse Theory, Cobordism Categories, and Positive Scalar Curvature«

Abstract:
In this talk I will construct a cobordism category consisting of manifolds equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. My main result identifies the homotopy type of the classifying space of this cobordism category with that of the infinite loopspace of a certain Thom spectrum. This result can be viewed as an analogue of the celebrated theorem of Galatius, Madsen, Tillmann and Weiss. In the second part of the talk I will show how to use the cobordism category to probe the homotopy type of the space of positive scalar curvature metrics on a closed, spin manifold of dimension ≥ 5. This construction uses a parametrized version of the Gromov-Lawson construction developed by Walsh and Chernysh. Our main result detects many non-trivial homotopy groups in the space of positive scalar curvature metrics and gives an alternative proof and slight extension of a recent breakthrough theorem of Botvinnik, Ebert, and Randal- Williams.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Bernhard Hanke
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



wwwadm@Math.Uni-Augsburg.DE,    Do 6-Jul-2017 10:39:38 MESZ